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apocalyptic n.  and  nude n.

First numbers that belong to both sets:

222, 224, 312, 366, 384, 612, 624, 648, 666, 824, 848, 864, 1128, 1155, 1164, 1212, 1224, 1416, 1424, 1464, 1488, 1515, 1626, 1644, 1692, 1715, 1722, 1944, 2212, 2222, 2224, 2226, 2262, 2316, 2322, 2364, 2448, 2622, 2824, 3126, 3132, 3144, 3162, 3171, 3195, 3276, 3288, 3312, 3324, 3333, 3336, 3339, 3366, 3384, 3393, 3432, 3444, 3492, 3555, 3612, 3648, 3717, 3816, 3864, 3888, 3924, 3996, 4112, 4128, 4144, 4164, 4184, 4212, 4244, 4344, 4368, 4392, 4412, 4416, 4424, 4464, 4488, 4632, 4644, 4848, 4872, 4888, 4896, 4968, 5115, 5155, 5355, 5515, 5535, 5555, 5775, 6126, 6132, 6144, 6162, 6192, 6216, 6222, 6288, 6324, 6336, 6366, 6384, 6432, 6444, 6612, 6624, 6636, 6648, 6666, 6696, 6762, 6816, 6912, 6966, 6984, 7112, 7119, 7266, 7448, 7476, 7644, 7728, 7777, 7784, 8112, 8128, 8136, 8144, 8184, 8224, 8232, 8248, 8288, 8328, 8424, 8448, 8488, 8496, 8616, 8664, 8688, 8736, 8824, 8848, 8928, 9126, 9135, 9144, 9162, 9216, 9315, 9324, 9333, 9396, 9432, 9612, 9648, 9666, 9864, 9936, 9999, 11111, 11112, 11115, 11122, 11124, 11128, 11133, 11136, 11144, 11155, 11166, 11172, 11184, 11196, 11212, 11222, 11224, 11226, 11244, 11248, 11262, 11288, 11316, 11322, 11328, 11331, 11355, 11364, 11412, 11424, 11436, 11444, 11448, 11488, 11515, 11535, 11555, 11616, 11622, 11664, 11676, 11688, 11711, 11824, 11832, 11848, 11872, 11888, 11916, 12112, 12122, 12124, 12126, 12128, 12132, 12144, 12162, 12168, 12212, 12216, 12222, 12224, 12244, 12248, 12264, 12288, 12312, 12324, 12336, 12384, 12412, 12424, 12432, 12444, 12448, 12488, 12612, 12624, 12636, 12648, 12666, 12712, 12726, 12768, 12816, 12824, 12848, 12864, 12888, 12924, 12996, 13113, 13116, 13122, 13128, 13131, 13155, 13164, 13212, 13224, 13236, 13248, 13266, 13272, 13311, 13326, 13332, 13335, 13344, 13362, 13368, 13377, 13392.

Some larger examples :